Two-sided hitting time of Brownian motion@Math-fun An event is a set of outcomes to which a probability can be assigned. In particular, $\{|W(t)|>a\}$, $\{T_a\le t\}$ and $\{|W(t)|>a\text{ and } T_a\le t\}$ are events, but $\{|W(t)|>a| T_a\le t\}$ is not, since it doesn't refer to a particular set of outcomes.